Anisotropic multipole moments

There have been many attempts to formulate a procedure to avoid it and both a posteriori and a priori schemes are available. The counterpoise approach (CP) (Boys and Bemardi, 1970) and related methods are the most conunon a posteriori procedures. Although this technique represents the most frequently employed a posteriori procedure to estimate this error, several authors have emphasised that the method introduced by Boys and Bemardi does not allow a clear and precise determination of the BSSE. The addition of the partner s functions introduces the "secondary superposition error" a spurious electrostatic contribution due to the modification of the multipole moments and polarizabilities of the monomers. This is particularly important in the case of anisotropic potentials where these errors can contribute to alter the shape of the PES and the resulting physical picture (Xantheas, 1996 and Simon et al., 1996). 

Mulder F, Van Dijk G, Van der Avoird A (1980) Multipole moments, polarizabilities and anisotropic long range interaction coefficient for N2. Mol Phys 39 407 125... 

So far only the minimal multipole moments and their contribution to the j, a., and (t2) values have been considered. However, they are not the only manifestations of the degeneracy in the characteristics of the absorption and Raman spectra under consideration. For instance, an important additional contribution to the torque can arise because of the anisotropy of the dispersion interaction between the molecules owing to the nonzero matrix elements of the anisotropic components of the polarizability tensor, i.e., the anisotropy of the cubic symmetry molecules in degenerate states. 

Electrostatic multipole moments of molecules, i.e., dipoles, quadrupoles, or octupoles, can also be obtained from QM wave functions. Methods like distributed multipole analysis (DMA) [84] or AIM [85] assign multipole moments to each atom or to specified sites of a molecule. The DMA method estimates multipole moments from QM wave functions and the highest obtained multipole moment depends on the basis set used. There are no limitations in this method on number or position of the multipoles anisotropic effects due to lone pairs or n electrons can also be considered. 

The familiar expressions for other permanent electrostatic interactions in terms of T-tensors [28] and spherical harmonics can be found elsewhere [3]. Early simulation studies placed the permanent moments within a spherical LJ-core [29]. This generalized Stockmayer potential is now frequently used as a basic model to examine the effects of boundary conditions in simulations of polar fluids [30]. In the simulation of "realistic" liquids it is now more usual to graft the multipole moment onto an ISM core. The first simulations of this type of model involved a diatomic LJ-core and a permanent quadrupole to model Na and Bra [8, 12]. The point dipole interaction has also been used with a non-spherical core to model HF [31]. This particular simulation also included the quadrupole-dipole (0 j) and quadrupole-quadrupole (66) interactions. Point moments are readily included in an m.d. simulation. For linear molecules acting with a central anisotropic potential the force on molecule i is given by [32]... 

Quantitatively, we expect the temporal response of a solvent to be governed by the dynamics of the translation and reorientation of its molecules. This response changes the interaction of the anisotropic charge distribution of the solute, as characterized by the multipole moments (dipole, quadrupole, etc.) of its charge distribution, with the multipole moments of the solvent molecules. In a polar solvent we can seek to relate the time scale of the solute s reorientation dynamics to the frequency dependence of the dielectric constant in the spectral region corresponding to nuclear motions. ... 

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